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# Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

*Proceedings of the 20th International Conference on Artificial Intelligence and Statistics*, PMLR 54:121-129, 2017.

#### Abstract

A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal- factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model is adapted for online learning, which allows dictionary learning on large data sets. After KFA is introduced, the model is extended to a deep convolutional tensor-factor analysis, supervised by a Bayesian SVM. The experiments section demonstrates the improvement of KFA over vectorized approaches (e.g., BPFA), tensor decompositions, and convolutional neural networks (CNN) in multi-way denoising, blind inpainting, and image classification. The improvement in PSNR for the inpainting results over other methods exceeds 1dB in several cases and we achieve state of the art results on Caltech101 image classification.